Zeitz The Art & Craft Of Problem Solving
Introduction
Zeitz The Art & Craft Of Problem Solving is a book written by Paul Zeitz, a professor of mathematics at the University of San Francisco. The book is aimed at students and professionals who want to improve their problem-solving skills in various fields, especially mathematics and science. The book provides a comprehensive guide to solving problems, developing strategies, and improving critical thinking skills.
Chapter 1: What is a Problem?
In this chapter, Zeitz defines what a problem is and distinguishes between routine and non-routine problems. He explains that non-routine problems require creative thinking and strategies that are not immediately obvious. He also discusses how to identify the underlying concepts and principles of a problem and how to break it down into manageable parts.
Chapter 2: Strategies for Problem Solving
In this chapter, Zeitz provides various strategies for problem-solving, such as brainstorming, guessing and checking, working backwards, and looking for patterns. He also emphasizes the importance of developing problem-solving habits, such as being systematic, being persistent, and being flexible.
Chapter 3: Tools for Problem Solving
In this chapter, Zeitz introduces various tools for problem-solving, such as diagrams, graphs, and tables. He explains how to use these tools to visualize problems and to organize information. He also discusses the importance of using mathematical symbols and notation to express ideas precisely and concisely.
Chapter 4: Number Theory and Algebra
In this chapter, Zeitz discusses various topics in number theory and algebra, such as divisibility, primes and composites, modular arithmetic, and polynomials. He provides examples of problems that can be solved using these topics and explains how to apply the strategies and tools discussed in the previous chapters.
Chapter 5: Geometry
In this chapter, Zeitz discusses various topics in geometry, such as angles, triangles, circles, and transformations. He provides examples of problems that can be solved using these topics and explains how to apply the strategies and tools discussed in the previous chapters.
Chapter 6: Combinatorics and Probability
In this chapter, Zeitz discusses various topics in combinatorics and probability, such as counting, permutations and combinations, and probability theory. He provides examples of problems that can be solved using these topics and explains how to apply the strategies and tools discussed in the previous chapters.
Chapter 7: Number Theory Revisited
In this chapter, Zeitz revisits number theory and discusses advanced topics, such as Diophantine equations, continued fractions, and the Chinese Remainder Theorem. He provides examples of problems that can be solved using these topics and explains how to apply the strategies and tools discussed in the previous chapters.
Chapter 8: Inequalities
In this chapter, Zeitz discusses various types of inequalities, such as arithmetic mean-geometric mean inequality, Cauchy-Schwarz inequality, and Jensen's inequality. He provides examples of problems that can be solved using these inequalities and explains how to apply the strategies and tools discussed in the previous chapters.
Chapter 9: Sequences and Series
In this chapter, Zeitz discusses various topics in sequences and series, such as arithmetic and geometric sequences, telescoping series, and power series. He provides examples of problems that can be solved using these topics and explains how to apply the strategies and tools discussed in the previous chapters.
Chapter 10: Limits and Continuity
In this chapter, Zeitz discusses the concepts of limits and continuity and their applications in calculus. He provides examples of problems that can be solved using these concepts and explains how to apply the strategies and tools discussed in the previous chapters.
Conclusion
Zeitz The Art & Craft Of Problem Solving is an excellent resource for anyone who wants to improve their problem-solving skills. The book provides a comprehensive guide to solving problems in various fields, especially mathematics and science. It teaches the reader how to develop strategies, improve critical thinking skills, and use various tools to solve problems. The book is written in a clear and concise style and provides numerous examples and exercises to reinforce the concepts learned. Whether you are a student or a professional, this book will help you become a better problem solver.